The Other Kind of Confirmation
(aka In Praise of Instance Confirmation)
Michael Strevens
Draft of April 2006
Abstract
It is argued that the relation of instance confirmation has a role to play in scientific methodology that complements, rather than competing with, a modern account of inductive support such as Bayesian confirmation theory. When
an instance confirms a hypothesis, it provides inductive support, but it also
provides two things that other inductive supporters normally do not: first, a
connection to “empirical data” that makes science epistemically special, and
second, inductive support not only for the hypothesis as a whole, but for its
parts. Further, when it is conceived in the right way, instance confirmation
can duck the arguments most often thought to refute it. A causal account of
instantiation, thus of instance confirmation, is offered that looks to deliver on
all of the foregoing promises.
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1.
Introduction
Of accounts of scientific confirmation, Bayesianism is surely the current champion, while instantialism is widely regarded as a hopeless relic. I want to make
a case for instantialism, not as a rival, but as a complement to Bayesian confirmation theory (or if Bayesianism should fall, as a complement to whatever
theory of confirmation comes to play Bayesianism’s present role).
I will not merely be pointing out that, on the Bayesian or any other view,
a hypothesis’s confirmers usually include among their number its positive instances. Everyone knows this already.
I will rather argue that there are two quite different, though systematically related, inductive relations between evidence and theory, either of which
might properly be called confirmation. Bayesianism provides a rather good
account of the weaker of these two relations; a certain sort of instantialism
provides, I think, the correct account of the stronger.
The two relations are not in any way incommensurable: on the contrary,
they are interlocking parts of a single inductive system, and indeed, if things
go well, the stronger relation is to be defined partly in terms of the weaker
relation.
I call the relations B-confirmation and I-confirmation. The ‘B’ is for Bayesianism and the ‘I’ for instantialism, but these are just mnemonics: nothing about
the notion of B-confirmation presupposes the involvement of subjective probability, and nothing about the notion of I-confirmation presupposes the involvement of instantiation. Bayesian confirmation theory should, then, be
thought of as a particular account of B-confirmation, and instantialism as a
particular approach to understanding I-confirmation.
This paper is structured around two considerations that give us reason—
so I argue—to posit the existence of two quite different kinds of confirmation
relation. The first consideration arises from Hempel’s argument that confirmation flows along the entailment relation from entailer to logical consequence
(section 3). The second focuses on a narrow but supremely important sense in
which evidence can be empirical (section 4). After presenting these considerations, I sketch an instantialist account of the stronger variety of confirmation
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relation, that is, of I-confirmation. Let me begin with the briefest of overviews
of the Bayesian and instantialist approaches to confirmation.
2.
Two Theories of Confirmation
On the instantialist theory of confirmation—Hempel (1945) is my paradigm—
there are two ways that a hypothesis can be confirmed. First, hypotheses are
directly confirmed or disconfirmed by their instances—if they are deterministic, they are of course confirmed by their positive instances and disconfirmed
by their negative instances.1
Second, hypotheses are confirmed or disconfirmed if they stand in the
right sort of logical or semantic relation to a hypothesis that has been directly
confirmed or disconfirmed. According to Hempel’s consequence rule, for example, when a set of hypotheses is confirmed, their logical consequences are
also confirmed. All confirmation is triggered by instance confirmation, then,
but a hypothesis can be confirmed by a piece of evidence that is not one of its
instances, by way of a confirmation transmission rule such as the consequence
rule.
Hempel’s account is perhaps best known for its satisfiability theory of instantiation, on which a hypothesis of the form All Fs are G has as an instance,
and thus is confirmed by, an observation of an object that is either not F or is
both F and G. This account will play no role in the present paper.
On the Bayesian approach to confirmation, a hypothesis h is confirmed by a
piece of evidence e just in case the receipt of e raises the subjective probability
of h, that is, just in case
Pr(h|e) > Pr(h)
The evidence e disconfirms h just in case Pr(h|e) < Pr(h).
A note on evidence: I follow Hempel and the Bayesians in taking the evidence, in what follows, to be an observation statement, that is, a proposition
1. If they are statistical, their confirmation or disconfirmation is a matter of comparing the
ratio of positive to negative instances with the ratio predicted by the hypothesis. The question
how to go about this comparison is not one on which I take a stand in what follows.
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spelling out some aspect of the observable world—the blackness of a particular raven, the value of particular readout, and so on. The evidence might
equally be regarded as the state of affairs represented by the observation
statement; this fits well with an instantialist approach, since it is natural to take
the blackness of the raven itself, not a statement of such, as what instantiates
All ravens are black. What evidence is not is some object in all its particularity,
such as an individual black raven. That is, though the evidence may be an observed worldly state of affairs—the blackness of a particular raven—it cannot
be the raven itself. The same goes, in what follows, for instances. It is a raven’s
combined ravenhood and blackness (or an observation statement that specifies the coinstantiation of these properties) that instantiates the hypothesis,
not the raven itself.
3.
Inductive Support versus Inductive Saturation
When certain aspects of Hempel’s motivation for adopting an instantialist view
are properly understood, I will argue, it is apparent that Hempel is seeking to
explicate a kind of inductive relation that is quite distinct from the relation
formalized by Bayesian confirmation theory.
Instantialism requires what I called in the previous section rules for the
transmission of confirmation. Hempel (1945) considers in particular two possible rules, the consequence rule and the converse consequence rule.2 Notoriously, the rules cannot be endorsed simultaneously, and Hempel opts for the
consequence rule (described in section 2). The details, though germane to the
present discussion, are omitted here for reasons of space. My principal interest
is Hempel’s justification of his decision to opt for the consequence rule:
Any . . . consequence [of a hypothesis] is but an assertion of all or
part of the . . . content of the original [hypothesis] and has therefore
2. The rules are first introduced as conditions of adequacy for any account of confirmation,
but Hempel’s intention is to put them to use as transmission rules; in his formulation of instantialism, the consequence rule is the one and only rule of transmission.
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to be regarded as confirmed by any evidence which confirms . . .
the latter (Hempel 1945, 31).
In this passage Hempel supposes that, when a piece of evidence confirms a
hypothesis, it provides evidential support for every part of the hypothesis.
To a Bayesian, this constitutes an oversight of Oedipal proportions: it is
not only possible, but extremely common, for a piece of evidence to confirm
a hypothesis by inductively supporting one, but not all, of its parts. To see
this, simply take evidence e that confirms hypothesis h, then choose another
hypothesis g that is intuitively irrelevant to e and h. (You might formalize
this irrelevance by requiring that g be independent of h conditional on e; see
Fitelson (2002).) On the Bayesian approach, confirmation is probability-raising.
Since e raises the probability of h, it also raises the probability of hg, for an
irrelevant g. Informally, if your confidence in h increases, and g has nothing to
do with h, then your confidence in hg ought to increase, since you are surer
than before of the first conjunct and no less (or more) sure of the second.
Thinking of hg as a single hypothesis, then, you have a case where e confirms
a hypothesis by confirming one part of the hypothesis but not the other.
How could Hempel have failed to recognize this possibility? Has the introduction of probabilistic thinking to confirmation theory so clarified the subject
matter that what seemed compelling to the ancients is immediately apparent
to us as an elementary error?
This is hardly plausible, considering that it was Hempel himself who introduced the problem of irrelevant conjuncts to confirmation theory. I propose
that what Hempel intended his instantialism to capture was an evidential relation to which the presupposition inherent in his justification of the consequence rule applies. In Hempel’s idiolect, a piece of evidence cannot be said
to confirm a hypothesis unless it provides inductive support for all its parts.
This is, obviously, a stronger notion of confirmation than the Bayesian version,
on which evidence can confirm a hypothesis by providing support for only
one of its parts.
What we have, then, are two classes of inductive relation. I call the first
and weaker relation inductive support. It is the kind of relation that Bayesians
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attempt to explicate. In what follows, at any rate, I take inductive support
and probability increase to amount to more or less the same thing, so that a
piece of evidence inductively supports a hypothesis just in case it increases the
probability of the hypothesis. Evidence may inductively support a hypothesis,
then, without supporting all of its parts.
The second and stronger relation I call inductive saturation. A piece of
evidence inductively saturates a hypothesis just in case it inductively supports
all of its parts, and thereby supports the hypothesis as a whole.3
While the Bayesian notion of confirmation is a support relation, the confirmation notion pursued by Hempel is, I suggest, a saturation notion. Further,
instantialist approaches to confirmation ought to be interpreted as, and are
generally quite suitable for, explicating a saturation relation. The instantialist
confirmation relation sketched in section 5, in particular, ought to be regarded
as such. The difference between B-confirmation and I-confirmation is in part,
then, that the latter but not the former is a relation of saturation; for the other
differences, see sections 4 and 5.
Why think that inductive scientific reasoning needs something more than
inductive support? Why think that confirmation theory should be concerned
with inductive saturation, so much so that the label confirmation might just as
well be applied to saturation relations as to relations of support?
Before I give an answer, let me emphasize that to be concerned with saturation is not to be unconcerned with support. Science needs an inductive
support relation at least as much as it needs a saturation relation—obviously
so, since saturation is characterized in terms of support. In what follows I
make a case for the absolute, not the relative, importance of saturation: the
newfound status of saturation should in no way be regarded as detracting
from the status of support. My goal, recall, is not to argue that the Bayesian
theory fails to capture the true nature of confirmation, but rather to argue that
there are two kinds of inductive relations, each scientifically important enough
in itself that it might be called confirmation. Bayesianism gives a good account
3. Support of all the parts is not quite sufficient for support of the whole. The clause after
the thereby is not merely a clarification, then, but a part of the definition of saturation.
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of one of these relations; my point is that we need to attend carefully to the
other, as well.
What, then, is the special significance of saturation? I take my aim here to
be to show that scientists have a considerable interest in knowing that a piece
of evidence not only supports, but saturates, a hypothesis.
Scientific inference aims to do two things with the evidence. First, the
results of an empirical test should tell us, as far as possible, what to expect
from other such tests. Second, the results of an empirical test should tell us
what hypotheses and theories to believe, or to “accept”.
Consider all of the hypotheses and theories that predict (either by entailing
or by probabilifying) a given empirical datum. Given the two aims of science,
it is important to know
1. Which of the hypotheses satisfy the following condition: because of the
evidence, we have better reason than before to believe all the other
experimental predictions made by the same hypothesis, and
2. Which of the theories satisfy the following condition: because of the
evidence, we have better reason than before to believe all the other
parts of the same theory, and therefore, in time, to accept the theory as
a whole.
What we want to know, then, is that the evidence inductively saturates the
hypothesis and the theory (using an intuitive but uncontroversial notion of
parthood).
Why is support on its own not enough? To be told that the evidence
supports, but not that it saturates, a hypothesis, is to be told that you have
more reason to believe the hypothesis than before, while leaving open the
question whether you have reason to rely any more than before on some,
or perhaps many, of the hypothesis’s predictions. Such information is nearly
useless to you in pursuit of the first aim of science. Equally, to be told that
the evidence confirms, but not that it saturates, a theory, is to be told that you
have more reason to believe the theory than before, but to leave open the
question whether you have any more reason than before to believe some, or
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perhaps many, of the theory’s parts. Such information is nearly useless to you
in pursuit of the second aim of science. (Compare Glymour (1980).) To assess
the ultimate scientific significance of a piece of evidence, then, you need to
know which hypotheses and theories it saturates.
I am not saying, of course, that information about support is useless on
its own. Quite the contrary: after all, enough of the right kind of information
about support will entail the facts about saturation. My point is simply that the
evidence has a special significance for the theories it saturates, as opposed to
the theories it supports without saturation; science, then, has a special interest
in saturation.
I am also not saying that we can do with information about saturation
alone. Sometimes we must make decisions that turn on hypotheses that are
supported by some of the evidence, but not saturated by any of the evidence;
in such cases, we of course care about relations of unsaturating support. In any
case, it barely even makes sense to claim that we can get by with saturation
alone, given that the facts about saturation are in part constituted by the facts
about support.
The picture I have sketched so far is very simple. Suppose that you define
a relation of inductive saturation as suggested above:
e inductively saturates h just in case e inductively supports all of h’s
parts
using some preexisting inductive support relation, perhaps the Bayesian relation. The issue of parthood aside, the structure of the inductive saturation
relation is inherent in the structure of the support relation. The two are different relations, but the saturation relation as it were reduces to the support
relation (more exactly, to the support relation plus the facts about parthood).
You might even say that, although confirmation theory aims at two goals,
a support relation and a saturation relation, its method is, just as the Bayesians
implicitly suppose, the elucidation of single relation, namely, the relation of
inductive support. That would be to go too far. Even given all the facts about
support, there are interesting new things to say about how and when saturation emerges from support, that is, about which sorts of evidence tend to
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saturate which sorts of hypotheses, and why. Compare higher and lower level
sciences: even if all the biological facts are entailed by all the physical facts,
there are still many interesting things to say about the way in which the entailment works. Philosophers may disagree on whether such an entailment
relation exists, but they agree that even if it does, there is still work for the
biology department to do.
However, I do not want to make a big deal of this. Although it is a mistake
to overstate the simplicity of the picture I have sketched, it is nevertheless unquestionably quite straightforward: B-confirmation is inductive support, and
I-confirmation is simply saturating B-confirmation.
The situation becomes more complicated in the next section, where I propose that I-confirmation—the relation that Hempel and others seek to capture
using the notion of instance confirmation—is characterized in terms of a narrower kind of inductive support than B-confirmation.
4.
Scientific Exceptionalism
Science is different—and better, if only at figuring out what is really going
on. Why? It might be white coats and expensive machinery. It might be the
sheer intellectual power of its practitioners. It might be a culture of “organized
skepticism”. It might be an undying commitment to the truth. It might be a
mix of these things.
But at least as important, in the estimation of many philosophers, is that
science is especially sensitive, and in the right sort of way, to the “empirical
data” (using empirical in a sense narrower than is usual in philosophy). Other
systems of knowledge production—the interpretation of sacred texts, the construction of conspiracy theories, perhaps certain aspects of folk medicine, and
of course philosophy—may make arguments, both inductive and deductive,
as sophisticated as those found in science; they may be, in some cases, just as
well funded; their practitioners may have equally subtle minds; yet they are by
comparison with science abject failures because they do not assign the central
role that science does to empirical testing.
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You might hope that the theory of confirmation would provide an account
of this “empirical testing” that makes science so exceptional in both senses of
the word. The Bayesian notion of confirmation will, in that case, disappoint
you. Bayesianism aims to elucidate the rules of inductive inference wherever
it is found. Thus the Bayesian’s inductive support relation is instantiated wherever there is competent inductive (and indeed, deductive) argumentation in
any of the fields of human inquiry enumerated above. How could it not be?
Whatever you think of Biblical scholarship, the unmasking of the Bavarian Illuminati, or counterpart theory, you must admit that they make use of inductive argument. The practitioners of these pursuits can be assigned coherent
subjective probability functions, and their reasoning can be interpreted and
evaluated as conditionalization according to the probabilities assigned. The
same is neither more nor less true of science. Bayesian confirmation theory is
thus not in a position, and does not aspire to be in a position, to distinguish
on logical grounds between the kind of reasoning found in science and the
kinds found in other pursuits.
Let me elaborate, focusing now on science alone. A scientist may come
to believe (or accept, or assign a high subjective probability to) a hypothesis
for many different kinds of reasons. She may (as noted above) find the hypothesis asserted by a reliable textbook, or by a reliable colleague. She may
infer the hypothesis, deductively or inductively, from some other hypothesis or
hypotheses she believes. Or she may put the hypothesis to the empirical test.
All of these procedures are legitimate sources of knowledge, but it is the last
of them that makes science special. Empirical evidence, whether produced by
experiment or gathered by fieldwork, is the epistemic lifeblood of science, and
the other sources of knowledge just mentioned are respected only insofar as
they lie on the path from empirical data to conclusion, and so have a claim to
carry the lifeblood themselves.
A natural way to capture this common belief about the nature and the
success of the scientific method is to posit a special kind of inductive support,
which I will call empirical inductive support. A paragraph in a textbook and an
experimental test may both lend inductive support to a hypothesis, but only
the former can give the hypothesis empirical support, or equivalently, only
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the former support relation belongs to that subclass of the inductive support
relations that are the empirical support relations. (I will remind you again that
the sense of empirical employed here is narrower than the usual philosophical
sense, on which any a posteriori inference, including inference from the printed
word, is empirical.)
I make the following proposals and claims:
1. Empirical support is important enough that we should consider coining
a sense of the term confirmation on which evidence e confirms h only
if e gives h empirical inductive support. In accord with my preexisting
terminological liberality, this use of confirmation may coexist with other
senses, such as the Bayesian’s B-confirmation.
2. The instantialists should be interpreted as aiming to give a theory of
empirical support. Their key doctrine: a deterministic hypothesis is
empirically supported by its positive instances (and empirically countersupported, as it were, by its negative instances).
3. The notion of empirical support may be profitably combined with the
notion of inductive saturation to provide a notion of empirical inductive
saturation, defined in the obvious way: e empirically inductively saturates h just in case e provides empirical support for all parts of h. The
relation of I-confirmation that I am pursuing in this paper is a kind of
empirical inductive saturation.
These proposals, you will see, generate the complication promised at the end
of section 3: they entail that I-confirmation is a certain, restricted kind of
inductive saturation, a kind defined in terms of an inductive support relation
distinct from B-confirmation—namely, empirical support.
Even if you accept that the Bayesian’s confirmation relation is not a relation
of empirical support alone, you might wonder whether Bayesianism will one
day be replaced by some other theory of inductive support that offers a more
empirical confirmation relation. I suggest not. It is not due to a quirk or weakness of Bayesian confirmation theory that its notion of confirmation embraces
non-empirical support. It is due, rather, to Bayesianism’s largely successful
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realization of its ambition to provide what might be called a universalistic conception of inductive support, that is, a conception that is instantiated wherever
correct inductive argumentation is found. Because some correct inductive reasoning is not empirical, no evidential relation can be both narrowly empirical
and universalistic.
What is the nature of empirical support, and why is it so important to
science? I will not provide an entirely general answer to this question, for the
following reason: the particular kind of instantialism I advocate in this paper is
based on a subclass of empirical support that I call causal-empirical support,
and I wish to restrict my attention to this subclass. In the next section, after
introducing my instantialism, I will have a characterization of causal-empirical
support, and I will say a few words about its epistemological significance.
Two remarks before I turn to instantialism proper. First, you might try to
capture what is especially “empirical” about science without positing a special
relation of empirical support. A Bayesian, for example, might point to the important Bayesian convergence theorems to demonstrate that enough of the
right sort of evidence will create a convergence of opinion. Such a move cannot, I think, succeed. The train of evidence that brings about the convergence
might just as well be, for all the mathematics of convergence cares, the utterances of concordant prophets as a stream of empirical data. (I would say more,
but space is at a premium.)
Second, note that Hempel’s stated motivations for instantialism include a
concern with empirical support as well as a concern with inductive saturation—
or so it can be argued. Because the argument depends in part on properties
of empirical support discussed in the next section, I defer the topic until then.
I have identified two properties of evidential relations that are of particular interest to the scientific enterprise, and that are distinct from the Bayesian
confirmation relation: the property of being a relation of inductive saturation,
and the property of being a relation of empirical support. The instantialist
notion of confirmation, I propose, attempts to unite these two, by offering an
evidential relation that combines saturation and empirical support in the obvious way: evidence e instance confirms a hypothesis h only if e empirically
supports all parts of h. (Note that the converse does not hold: instance confir12
mation does not capture every kind of empirical support, or at least, I will not
try to argue that it does.)
Taking a step back, I have now provided characterizations of two distinct notions of confirmation. On the one hand, you have a confirmation
relation that amounts to a universal inductive support relation, that is, the
relation that obtains wherever a good inductive argument is found. This is
what I call B-confirmation, in honor of Bayesianism’s claim to provide an especially powerful theory of universal inductive support. On the other hand,
you have a confirmation relation that is a kind of saturating empirical support,
which I call I-confirmation both for historical reasons—it is the kind of relation
that I suppose Hempel was aiming to capture with his instantialist theory of
confirmation—and for more forward-looking reasons, namely, my claim that a
certain account of instance confirmation, distinct from Hempel’s, does a very
good job of capturing I-confirmation.
Let me sketch a simplified version of the instantialism that I favor.
5.
A New Instantialism
5.1
Instantiation
What follows is a sketch of an attractive but unsophisticated account of instantiation. The account is restricted in scope. It applies only to the instantiation
of causal hypotheses, and in its current formulation, only to causal hypotheses
of the form All Fs are G. This is not, I think, so great of a narrowing of focus
as it seems. Most scientific hypotheses are causal. For example, the raven
hypothesis—All ravens are black—is not the simple empirical generalization
that Hempel took it to be. Properly understood, it does not say merely that
everything that is a raven is also black. Rather, it says that there is a certain
mechanism, present in or in the vicinity of all ravens, or at least all normal
ravens, that causes blackness. (I do not require that the property of ravenhood
itself do the causing; that would be to ask too much (Strevens manuscript c).)
I assume that we associate with every causal hypothesis a single mechanism in virtue of which the something about F causes G-ness. Our description
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of that mechanism may be radically incomplete, but we do have in mind some
sort of characterization of the mechanism, however rudimentary. Call this description the hypothesis’s associated causal model.
The effect of the associated model is to turn a hypothesis into a small, selfcontained causal theory. Observe that, even if a hypothesis is correct in the
overt causal claim it makes, it may be defective in the sense that its underlying
theory—its associated causal model—fails to reflect the causal facts: either it
misrepresents the true mechanism, or there is no single true mechanism at all,
but rather several mechanisms all having the same effect.
Now the account of instantiation. For simplicity’s sake, I will talk as though
it is things that instantiate hypotheses, though as noted in section 2, it is more
accurate to say that states of affairs or propositions are the instances.
An object is a positive instance of a hypothesis of the form All Fs are G just
in case
1. It is F and G, and
2. The associated causal model’s conditions for operation are satisfied.
By the model’s conditions for operation, I mean a certain specified set of conditions necessary for the modeled mechanism to cause G-ness. These are what
are sometimes called ceteris paribus conditions; they include background conditions for the mechanism’s operation, conditions that rule out any interference
with the operation, and conditions that rule out the later reversal of the mechanism’s output, that is, that specify that no later process destroys the G-ness of
the F in question. (It is somewhat awkward to call this last kind of requirement
a condition for the mechanism’s operation; rather, it is a condition required for
the sustenance of the end-product of the mechanism’s successful operation;
an example is provided below.)
The set of operation conditions specified by a model, thus required for
instantiation, need not be in any sense complete. Why not? Among other
things because, were the conditions of operation to be necessary and sufficient
for the operation of the mechanism, there could be no negative instances. A
negative instance of the canonical hypothesis All Fs are G is an F for which the
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conditions of operation obtain, but which is not G. Clearly, there could be no
negative instances if the operation conditions’ obtaining entailed the presence
of G. It is a tricky question what the relation is between the conditions for
operation and the causal model itself. It is on this very issue, indeed, that the
simple account of instantiation presented above departs from what I believe
to be the true account (Strevens manuscript a).
The account of instantiation I have offered differs from Hempel’s satisfiability account (section 2) in two respects. First, and more shallowly, it allows
only Fs to be instances, where Hempel counts all non-Fs as instances as well.
Second, it includes the causal condition, condition (2) (which presupposes the
F-ness of the instance).
Let me say something more about this condition (2). A black raven, you
will see, instantiates the raven hypothesis (on a causal interpretation) just in
case its blackness is possibly due to the causal model associated with the law.
A raven dyed black is therefore not an instance of the law. Why? While there
is a mechanism that is responsible for the blackness of a dyed raven, it is very
different from the mechanism described by the raven hypothesis’s associated
causal model: even the most naive ornithological theorist has in mind a mechanism in which the causation is an internal, biological matter.4 Technically,
what has gone wrong in this case is that a certain condition required for the
operation of the natural raven blackness mechanism has been violated, a condition of the sort that requires that the mechanism’s operation not be later
undone or reversed.
Looking ahead to confirmation, that the dyed raven is no instance is quite
encouraging, since you would not count the color of such a bird as evidence
for the law. Likewise, a raven bleached white is not a negative instance of the
law, and so is not counted as evidence against the law.
A white shoe, I am sure you can see, does not even begin to satisfy the
criteria for instantiating the raven hypothesis; its color clearly has nothing to
do with the hypothesis’s associated causal model. Why no paradox? Hempel’s
route to the raven paradox assumes the logical equivalence of the hypotheses
4. There is good psychological evidence for this claim; see Strevens (2000).
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All ravens are black and All non-black things are non-ravens. On the causal gloss
given here, these hypotheses mean quite different things: the former makes
a claim about the causation of blackness in ravens, while the latter makes
a (patently false) claim about the causation of non-ravenhood in non-black
things. (Although a white shoe is not an instance of the raven hypothesis,
it will in certain circumstances provide some slight inductive support for the
hypothesis, by the usual Bayesian arguments.)
I define direct instance confirmation in the same way as Hempel (section 2):
a deterministic hypothesis is directly confirmed by its positive instances and
directly disconfirmed by its negative instances. You will recall that Hempel
then uses a transmission rule, the consequence rule, to allow the confirmation brought by a piece of evidence to percolate from directly confirmed hypotheses to other, logically related, propositions (specifically, the logical consequences of the directly confirmed hypotheses). I will discuss transmission
shortly. I first want to vindicate my claim that if e directly confirms h—if e is an
instance of h in the sense just described—then e empirically supports all parts
of h.
I begin by showing that an instance saturates the hypothesis, that is, that it
inductively supports all parts of the hypothesis, given the appropriate notion
of parthood. I then ask, in a separate section, whether the support offered to
the parts by an instance is empirical.
5.2
Saturation
An instance of a hypothesis saturates the hypothesis if it provides inductive
support for all parts of the hypothesis. What are the parts of a hypothesis?
In arguing for the importance of saturation in section 3, I suggested that scientists are particularly interested in two classes of hypothesis “parts”: first, a
hypothesis’s various predictions, and second, the various sub-hypotheses of
which it is composed.
In the case of causal hypotheses, I interpret these parts (with something
of a stipulative flourish) as follows. The predictions of a causal hypothesis are,
loosely speaking, its instances. More exactly, the prediction of a hypothesis
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such as All Fs are G is a conditional claim: any F for which the associated causal
model’s conditions of operation are satisfied will be G. The instances are, as it
were, not the predictions themselves but the realizations of the predictions—
but I will not strive to maintain this distinction.5 The sub-hypotheses of a
causal hypothesis are the propositions that together make up the description
of its putative underlying mechanism, that is, its associated causal model. (If it
strikes you as peculiar to count the model as a part of the hypothesis, I think
you are right. As foreshadowed above, it would be better to call the model
a theory, and to think in terms of the predictions and sub-hypotheses of the
theory. But having written in terms of hypotheses throughout the paper so
far, I prefer to avoid a sudden terminological switch.)
An instance of a hypothesis saturates the hypothesis, then, if first, it provides inductive support for the hypothesis’s being instantiated in any other
situation to which it applies, and second, it provides inductive support for all
parts of its casual model. Let me show that, intuitively, saturation does occur—
intuitively, because I am not working with any particular theory of inductive
support.
Begin with the parts of the associated causal model. I make the following
important assumption: everything mentioned in the model plays an essential
part in the putative causal processes that result in the hypothesis’s instantiation. For example, every part of the model for the blackness mechanism
in ravens needs to be present, according to the story told by the model, for
ravens to get their color, or at least raises the probability of their doing so, in
an appropriately causal way. As I have put it elsewhere, the parts of the model
must all be difference-makers (Strevens 2004, manuscript b).
Now, given that the causal model describes only difference-makers for the
instance—given that, had any of the the causal factors mentioned by the
model not been present, the hypothesis would not have been instantiated,
or at least, would have had a lower probability of being instantiated—the fact
5. To elucidate my concern: All ravens are black does not predict that any particular object
will be both a raven and black, but rather predicts of whatever particular objects are ravens,
that they will be black. It is for this reason strictly speaking incorrect to say that any particular
instance is per se predicted by the hypothesis.
17
of instantiation gives us more reason than before to think that the factors are
present, just as the model asserts. Thus an instance provides inductive support
for all parts of the model, as desired.6 (An important objection to this line of
reasoning will be considered shortly.)
Next, the saturation of the “parts” of a hypothesis that are its predictions.
An instance of the causal hypothesis All Fs are G gives you reason to believe,
by the argument in the previous paragraph, in the existence in or around Fs
of a certain mechanism, namely, the mechanism described by the hypothesis’s
associated causal model. As such, it lends empirical inductive support to any of
the phenomena that such a mechanism tends to generate, or in other words,
to the hypothesis’s instances.
Let me consider an apparent difficulty with the argument for saturation:
the same piece of evidence that gives positive inductive support to an instance
or model-part for the reasons given above may also give it negative support for
some other reason, sufficient to cancel out the positive support. For example,
a piece of evidence might be an instance of two rival hypotheses that agree in
some of their predictions but not in others. By providing inductive support to
opposing pairs of predictions, the evidence will provide net inductive support
to neither. Or (perhaps less likely) the same factor whose presence is stipulated
by the causal model for one hypothesis may have its absence stipulated by
the causal model for another, so that evidence that is an instance of both
hypotheses is on balance neutral as to the factor’s presence.7
There are two ways to deal with this problem. First, you might relax the
criteria for saturation somewhat (at least in the context of the definition of
I-confirmation), saying that evidence that I-confirms a hypothesis must empir6. Compare and contrast Glymour (1980)’s technique for distinguishing parts of a theory that
are confirmed by a piece of evidence; whereas I hold that the parts of a theory describing the
causal difference-makers are confirmed, Glymour offers a purely syntactic criterion for the same.
7. There are, for example, two well known mechanisms causing thrombosis in women. One
involves the birth control pill; the other involves pregnancy, and thus the absence of the pill. The
fact of thrombosis in a particular patient therefore provides positive support for the patient’s
taking the pill along one path, but negative support along the other. The overall level of
inductive support depends, according to the usual Bayesian formula, on both the strength of
the support along the two paths and the base rates—essentially, the ratio of pregnant women
to women on the pill in the population from which the patient is drawn.
18
ically support most of its parts, or must empirically support its parts all other
things being equal.
Second (taking off, in effect, from the ceteris paribus hedge just suggested),
you could pay closer attention to the different senses in which one proposition
might be said to inductively support another. The standard Bayesian notion
of inductive support is an “all things considered” notion, on which evidence
e supports h only if the sum total of its inductive relevance to h is positive.
There may be more than one “inductive path” from e to h—e may be relevant
to h in more than one way, as in the examples above. An all-things-considered
measure of support aggregates the support over all the paths. (The aggregate
may not be a simple sum; see section 6.)
To say that e inductively supports h is not necessarily to say that e supports
h all things considered. It can also mean that e supports h along at least one
inductive path, without ruling out the possibility that the support is undone
by negative support along other paths. Thus it is not inconsistent to say: e
gives you reason to believe h, but it also gives you reason to disbelieve h; as a
result, e’s net impact is neutral or unfavorable to h. I propose that the inductive
support that an instance invariably lends a hypotheses’ parts is of this pathspecific variety. Then, I claim, the argument for saturation goes through.
In order to clarify matters, I will incorporate the notions of all-thingsconsidered and path-specific support into the definitions of B-confirmation
and I-confirmation, saying that e B-confirms h just in case e provides all-thingsconsidered inductive support for h, whereas e I-confirms h just in case e provides path-specific empirical support of some sort for all parts of h. However,
there exist broader notions of B-confirmation and I-confirmation that do not
impose these restrictions;8 my narrowing is primarily for expository purposes.
To sum up, then: if e is an instance of h, then e inductively saturates h,
or more exactly, e provides inductive support, in the path-specific sense, for
8. For example, there may be a useful notion of B-confirmation on which that fact that
e B-confirms h implies only that e provides path-specific support for h. What makes it
B-confirmation is that first, it does not imply saturation, and second, it is universal—wherever
there is inductive support there is B-confirmation. Since all-things-considered support implies
path-specific support, this notion of B-confirmation is strictly broader than the official notion
defined in the main text.
19
all parts of h, meaning its predictions and the components of its associated
causal model. Now to discuss the sense in which the support is empirical.
5.3
Empirical Support
What is empirical support, and why is it important? I will not offer a definition of empirical support. I take it that the instances of a hypothesis are its
paradigmatic empirical supporters: if there is such a thing as empirical support at all, then black ravens empirically support All ravens are black, black
holes empirically support Black holes exist, and so on. Although eventually,
someone will have to define empirical support and show that instances are
empirical supporters, this is very far from being an urgent problem.
Let me therefore simply stipulate that the instances of a hypothesis empirically support the hypothesis, and that they do so because of their intimate
causal relation to the hypothesis. Call this causal-empirical support. There may
be other varieties of empirical support; I put the matter aside for now.
The stipulation allows me to move immediately to what I take to be a
more interesting question: why is empirical support of special interest to, and
apparently especially desirable to, science? What, in particular, is good about
what I am calling causal-empirical support?
The question might be divided into two parts. First, why is causal-empirical
support a kind of inductive support? That is, why does a evidence that causalempirically supports a proposition also inductively support (in a path-specific
way, of course) that proposition? Second, what is special about this particular
variety of inductive support? What does causal-empirical support have that
other varieties of inductive support—at least the non-empirical varieties—do
not have?
I will not say much about the first question. There are as many ways to
show that causal-empirical support is inductive support as there are theories
of inductive support. A Bayesian, for example, can show that an instance of
a hypothesis will, as well as raising the probability of the entire hypothesis,
raise the probability of the parts of the causal model (ceteris paribus), and
so raise the probability of the predictions of the causal model (again ceteris
20
paribus). In a Bayesian or any other demonstration of the inductive power of
instances, the key fact is that the parts of the causal model jointly entail, or at
least physically probabilify, the instances.9
I should add that this sort of Bayesian derivation is not completely straightforward, because it involves splitting the change in the probability of the hypothesis part given the instance into different components, only one of which
reflects the path-specific support given to the hypothesis part by the instance
in virtue of its being an instance of that particular hypothesis. The ceteris
paribus hedges therefore pass over some fancy derivational footwork. For
an example of the technique of splitting an all-things-considered probability
change into path-specific components, see Strevens (2001).
To the second question, then: why is causal-empirical inductive support
somehow preferable to other, non-empirical forms of inductive support? The
answer, I think, is that causal-empirical support does not depend on auxiliary
hypotheses. This gives the causal-empirical support relation a considerable,
and valuable, degree of freedom from the local epistemic context. A particular degree of causal-empirical support is no stronger, inductively, than the
same degree of non-empirical inductive support—how could it be?—but has
a certain kind of objectivity that the scientific enterprise rightly values.
How is causal-empirical support context free? Begin with a kind of support
that is clearly not context free. Thinking David Lewis to be a great philosopher,
I am inclined to believe anything I read in On the Plurality of Worlds. Thinking
David Lewis to be a brilliant but perverse philosopher, you give endorsement
in the book no weight at all (perhaps even negative weight). We agree which
hypotheses are asserted in On the Plurality of Worlds, but we do not agree on
the inductive significance of the appearance for the hypotheses themselves,
because that significance depends entirely on an auxiliary hypothesis con9. It is not quite this simple, in the statistical case. For a Bayesian, to support a hypothesis h or
its parts, an instance must be probabilified by h to a greater degree than it is by the competing
hypotheses, weighted by prior subjective probability. A likelihood approach to statistical inference
finds a way to ignore these weights (by understanding support in a comparative way). More
generally, the nature of your favorite theory of inductive support will determine the caveats
and riders you will want to attach to the claim that instances provide path-specific inductive
support for their statistical hypotheses’ parts.
21
cerning the truth-tracking powers of Lewis’s philosophical faculties. To put
it another way, all paths from the evidence (appearance in the book) to the
hypotheses themselves goes by way of a further, quite distinct hypothesis.
Instances are not like this. There is an inductive route from an instance to
its hypothesis, and to the hypothesis’ parts, that does not make any detours,
essentially because a hypothesis’ associated causal model is sufficient in itself,
without auxiliaries, to entail or to physically probabilify its instantiation. (Reminder: on what it means to probabilify an instantiation, see note 5.) Thus
though we may disagree on a lot, we can agree on the causal-empirical support that an instance gives a hypothesis in a way that we cannot agree on
the support given a hypothesis by its assertion in On the Plurality of Worlds.
(Caveats shortly.)
It is this agreement, and its objective basis in entailment/physical probabilification, that gives causal-empirical support its value. Science is a social
enterprise. It cannot proceed efficiently without a high degree of consensus
on certain things, most of all consensus on the evidence and on the inductive
significance of the evidence.10 Now, if something like the Bayesian theory is
correct, there cannot be perfect agreement on the all-things-considered significance of the evidence. It is possible, however, for scientists to selectively
ignore, in public though perhaps not in private, the stickily subjective strands
of the inductive web in favor of the strands whose strength is equally appreciated by all. What I am calling causal-empirical support is a category of just
such strands—the most important category, I would say. If I am right, then the
facts about causal-empirical support constitute the principal intersubjective—
indeed, the principal objective—basis for the ongoing scientific evaluation of
theories.
As I remarked earlier, Hempel’s instantialism seems to have been motivated
in part by a similar concern. In arguing against hypothetico-deductivism (he
calls it the prediction criterion for confirmation), he complains that many of
a theory’s predictions, which all, according to hypothetico-deductivism, are
10. On some other matters, disagreement may be a virtue: see Kitcher (1993), chap. 8 on
the importance of cognitive diversity in science.
22
confirmers, go by way of auxiliary hypotheses. Hempel implicitly rejects a
common defensive reply, that what is confirmed is a conglomerate of theory
and auxiliaries. He wants the theory itself confirmed by the evidence, but not
by way of auxiliaries. Thus he insists that only instances can directly confirm.
(Hempel’s dislike of auxiliaries is not obviously motivated by the disadvantages
of auxiliaries I have cited here; you would not expect to find him exclaiming
that science is a social enterprise. But I conjecture that it is, in the end, based
on similar concerns.)
I mentioned some caveats on the objectivity of the empirical support relation. Even when confirmation is based around empirical support, it cannot be
entirely context free. One reason, which applies to Bayesians (but not, say, to
likelihood theorists), is explained in note 9. Another is that freedom from auxiliaries applies only to the inductive relation between instance and hypothesis.
But often auxiliaries are required to infer that you have observed an instance
at all. Why? Consider a causal hypothesis of the form All Fs are G. To infer
that you have an instance, you must infer that you have an F that is G, and for
which the associated mechanism’s conditions of operation held. If F, G, or any
of the conditions spelled out in the associated model are not directly observable, you will likely need auxiliary hypotheses to infer their obtaining. Even if
the inference from instance to hypothesis is context free, then, the inference
from observation to instance may not be.
Hempel avoids this problem by giving a theory that applies to hypotheses couched in observable terms only. Another prominent instantialist, Clark
Glymour, allows you to use the parts of the theory you are attempting to
confirm to infer the presence of unobservable instances—a technique he calls
“bootstrapping” (Glymour 1980). To take advantage of bootstrapping, however, you must build all of the auxiliaries you need—except, perhaps, those
that are known independently to be true, and thus concerning which there is
consensus—into the theory, resulting in the confirmation of a theory-auxiliary
conglomerate rather than of the theory alone. (Boot-strapping may in any case
be too liberal; see Christensen (1990).)
I have no magic bullet to offer. I can only echo the conventional wisdom:
use auxiliaries you can rely on. Seek to test auxiliaries independently of your
23
theory. And so on. Just because you cannot have independence from auxiliaries everywhere, however, is no reason to turn it down when you can get
it—and you can get it in the causal-empirical inferential step from instance to
hypothesis.
5.4
Transmission
I have defined a direct confirmation relation. Do I need a transmission rule
such as Hempel’s consequence rule? The closest viable equivalent to the consequence rule is something like the following:
If e directly confirms h, then e also confirms any part of h.
The validity of the transmission rule need not be postulated; it follows from
the transitivity of parthood (any part of a part of h is a part of h) and the
definition of I-confirmation in terms of saturating causal-empirical support, by
the following argument. Suppose that e I-confirms h. Then e causal-empirically
supports all parts of h. If g is a part of h, then by the transitivity of parthood,
all parts of g are parts of h, thus e causal-empirically supports all parts of g.
Consequently, e I-confirms g.
Such a transmission rule is of limited use, however. Suppose that e confirms
h, and that h is in turn a part of a theory t, but that e does not empirically
saturate t: there is some part of t that is not empirically supported by e. We
would like to know how to regard t in the light of e. The transmission rule
provides no help.
I propose to handle the problem in three steps. First, observe that it is not
a formal defect of instantialism if it has nothing to say about the evidential relation between t and e. After all, instantialism is a theory of I-confirmation, and
I-confirmation was never supposed to provide a universal theory of inductive
reasoning (see section 4).
Second, it can be argued that science has no principled interest in t as
a whole until it is saturated by some piece of evidence—since without such
evidence it is no more than either a conjunction of independently I-confirmed
hypotheses (if each of its parts is I-confirmed by some piece of evidence), or
24
the conjunction of one or more I-confirmed hypotheses with other hypotheses
having, as yet, no empirical basis (otherwise).
Third, when practical or decision-theoretic concerns demand that the possibility of t’s truth be taken into account, what is relevant is the total inductive
support lent by e to h, hence not the relation of I-confirmation but the relation of B-confirmation, which being universalistic always has something to
say about the impact of e on h. In short, from a practical point of view what
matters is the degree to which e B-confirms t; from a scientifically purist point
of view, what matters is what the available evidence I-confirms—so that if e
does not saturate t, then t does not yet matter.
6.
A Fatal Objection?
Consider a well-known argument due to I. J. Good. Suppose you know that
you have just been transported randomly to one of two worlds. Nine-tenths
of the first world’s birds are ravens, and nine-tenths of these are black. The
chance of a random bird’s being a black raven in this world is therefore 81%.
In the second world, one bird in ten is a raven, and all of these are black. The
chance of a random bird’s being a black raven in this world is therefore 10%.
You open your eyes. The first bird you see is a black raven. This is much more
likely in the first world than the second world, so the observation gives you
good reason to think that you are in the first, not the second world. In the
first world, however, not all ravens are black. Thus your observation of a black
raven has given you good reason to disbelieve that all ravens in your new
world are black. As Good rightly reasons, the black raven, uncontroversially
an instance of the raven hypothesis, provides strong inductive support for the
hypothesis’s negation (Good 1967).
It is natural to conclude that the black raven disconfirms the raven hypothesis, thus entirely undermining, in a paragraph, the instantialist approach to
confirmation, and furthermore, showing that it fails precisely because it neglects epistemic context.
The refutation of instantialism goes through, however, only if is supposed
25
that the sense in which Good’s black raven disconfirms the raven hypothesis
is identical to the sense in which instantialism holds that all instances confirm
their hypotheses. I, of course, deny this: Good’s raven B-disconfirms the raven
hypothesis, but instantialism is a theory of I-confirmation. To put the point
in terms of inductive support, Good’s raven bears negatively on the raven
hypothesis all things considered, but instantialism makes claims only about
path-specific empirical support. The evidence’s providing positive support for
a hypothesis along one path is quite consistent with its providing sufficient
negative support along other paths that the net effect is inductively undermining rather than affirming.11 (This is not, note, the defense mounted by
Hempel (1967). Hempel, I think, has universalistic aspirations for this confirmation relation—a serious error, on my approach.)
A question remains. The proponent of instance confirmation is committed to Good’s black raven’s lending positive inductive support to the raven
hypothesis along at least one path. But the significance of the raven seems to
be contained entirely in the information you have about your two worlds, by
way of which the raven disconfirms the hypothesis. Where does the putative
positive support go?
The answer is that it is “trumped” or completely overridden. Compare the
following simple case: h confers a high physical probability on e, but e together with background knowledge entails that h is false. In virtue of its conferring high physical probability on the evidence, the hypothesis is supported
by the evidence along one path. But in virtue of entailing, in conjunction with
background knowledge, the negation of the hypothesis, the hypothesis is refuted. These two evidential relations are not additive—their net effect is not
obtained simply by taking the sum of the parts. Rather, the latter, refuting
relation entirely nullifies the former. It is what some inductive logicians would
call a “rebutting defeater” (Pollock 1974).
11. More generally, there are two ways to deal Good-style counterexamples, that is, cases
where an instance B-disconfirms its hypothesis. First, you might show that the disconfirmation
is not empirical, that is, that the negative inductive support that secures the disconfirmation
is not of an empirical variety. Second, you might show that the negative inductive support
responsible for the disconfirmation of the hypothesis, while empirical, is not along the same
path in virtue of which the evidence is an instance of the hypothesis.
26
It is a challenge to discern a nullified support relation between evidence
and hypothesis in a purely all-things-considered inductive system such as
Bayesian confirmation theory. One hope is to examine certain counterfactual
B-confirmation relations, the relations that would exist if background knowledge were somewhat different. (Compare the similar solutions suggested to
the problem of old evidence in, for example, Howson and Urbach (1993).) I
regard this, however, as a weakness of Bayesian confirmation theory, rather
than as good reason to think that there is no sense to the notion of nullified
(or for that matter, path-specific) support.
7.
Conclusion
I have argued for the existence of two evidential relations: B-confirmation,
which is a relation of universalistic, perhaps all-things-considered, inductive
support, and I-confirmation, which is a relation of path-specific empirical inductive saturation. Both relations might be called the confirmation relation,
the first perhaps more reasonably in the context of decision theory or some
other practical pursuit, the second more reasonably in the narrower context
of scientific inquiry. From the existence of this distinction and the supporting
arguments, I draw several different kinds of conclusions.
First, not so much a conclusion as a piece of consciousness-raising: a theory
of confirmation does not have to be a universalistic theory of inductive support, that is, it does not have to account for every evidential relation in which
one proposition gives us good reason to believe or disbelieve another. Confirmation theory is a part of philosophy of science, and a far narrower relation,
of special interest to and significance for science, might be taken as its proper
area of inquiry—without in any way disparaging the enterprise, pursued by
Bayesians and others, of giving a complete theory of inductive reasoning.
Second, a historical conclusion: Hempel, Glymour, and other instantialists
should be viewed as providing, not an account of universalistic inductive support or B-confirmation, but an account of a more selective evidential relation,
one that is at the very least path specific. Their theories of confirmation make
27
the most sense, I think, when interpreted as accounts of I-confirmation, that
is, of a relation of saturating empirical support. This explains their favorable
attitude to the consequence rule, and even more important, their focus on
instances, which are after all—outside of the lab—a rather exclusive class of
inductive supporters.
That said, it must be admitted that Hempel sometimes writes as though
he is pursuing a universalistic notion of confirmation. In the introduction to
his classic paper on confirmation he says:
While criteria of valid deduction can be and have been supplied
by formal logic, no satisfactory theory providing general criteria
of confirmation and disconfirmation appears to be available so far
(Hempel 1945, 4).
Hempel’s pairing of confirmation and deductive logic in this passage suggests
that he envisages a theory of confirmation that is a theory of all inductive
inference. Further, as noted in the previous section, he declines to take the
non-universalist’s obvious way out of Good’s problem.
Third, confirmation theory can stand to pay far closer attention to actual
scientific method without surrendering its logical and epistemological compass. When real scientists talk about “the evidence”, they have in mind facts
bearing on their hypotheses in a very particular way, namely, through the relation of empirical support. The nature and importance of empirical support
in the scientific enterprise has suffered serious neglect in recent philosophy of
science, largely due to a focus on Bayesian universalism. But it is possible, as
Hempel and Glymour and section 5 of the present paper show, to investigate
empirical support without traducing the precepts of traditional epistemology,
that is, without abandoning your commitment to the precise and relatively formal specification of the underpinnings of the relevant evidential relations and
without renouncing as your paramount goal an explanation of their inductive
force.
Fourth, there is much work to be done in confirmation theory yet. The
account of instantiation given in section 5 is just a beginning. The topic of
empirical support ought to be revived. Work on empirical support might take
28
the more narrowly epistemological direction described in the last paragraph,
asking for example whether there are non-causal forms of empirical support,
but it might also set out in a broader methodological direction, asking about
the social function of the focus on empirical support in science. The Bayesian
ride has been a thrill, but it is time for something new.
Fifth, there is a lesson in all of this to be learned about inference to the
best explanation. Laws of nature and other sufficiently exalted generalizations
explain their instances; they are also confirmed by their instances. In the case
of causal generalizations, the explanation and the confirmation are in virtue
of almost the same facts, namely, the instance’s having been actually or apparently produced in accordance with an associated causal model. As the
actual/apparent dichotomy shows, the parallel is not exact: a false hypothesis
can be confirmed by its instances, but it cannot genuinely explain those instances. (A more precise parallel, then, is between confirmation and apparent
explanation.) But it is close enough, I think, to account for a part of our sense
that much scientific inference flows along a connection that is, when reversed,
explanatory.
29
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